An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term

Abstract

In this paper, an iterative algorithm to solve Algebraic Riccati Equations (ARE) arising from, for example, a standard H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem is proposed. By constructing two sequences of positive semidefinite matrices, we reduce an ARE with an indefinite quadratic term to a series of AREs with a negative semidefinite quadratic term which can be solved more easily by existing iterative methods (e.g. Kleinman algorithm in [2]). We prove that the proposed algorithm is globally convergent and has local quadratic rate of convergence. Numerical examples are provided to show that our algorithm has better numerical reliability when compared with some traditional algorithms (e.g. Schur method in [5]). Some proofs are omitted for brevity and will be published elsewhere.